Live Investing in US Corporate Bond Market During Economic Crisis

A- OverviewofBondMarket

Considering the current economic uncertainty in the UK economy – resulting from the fear of No-Deal Brexit negotiations, the future of this economy is undecided, therefore to invest in the US economy during this time of turmoil would prove more appropriate. Additionally, due to your risk neutral nature, investing in US Corporate bonds would provide larger returns given larger risk factors aligned with your target return of around 4% and your investment horizon of 10 years.

Therefore, the premise of investing in the US Corporate Market was set. Upon the request of investing in the US market, our aim is to provide you with the best portfolio within the US economy given the current economic climate. A corporate bond is a debt instrument representing the obligation of the corporation to pay coupon payments at predetermined dates and rates and redeem the principal value of the bond at its maturity. Money earned from the issue of the bond is used for long term debt financing. A corporate bond is said to be riskier than government bonds therefore interest rates are higher. 1

The US corporate bond market has grown dramatically over the last ten years. ‘Much of that increase has been concentrated in the investment-grade corporate bond market.’2

A reason why the corporate bond market has grown this much could be that investors anticipated an increase in interest rates during the year, as the Fed was expected to hike three times in 2017. 3

The bond market ‘delivered solid returns to fixed income investors in 2017’4 with single S&P rated A and BBB rated bonds dominating these high returns. Therefore, we have decided to invest in BBB rated bonds which provide larger returns whilst obtaining higher rating bonds (AA, AAA) which are safer bonds, reducing chances of default risk.

The US Corporate Bond Market has had a rocky start in 2018. ‘According to Moody’s Capital Markets Research Group, in the second quarter of 2018, bonds ‘rose by 3.3% year-over-year to $7.212 trillion.’ This was 0.6% lower than the first quarter and the smallest increase since final quarter of 2015 where growth rate was only 2.1%. In 2018, highly rated US corporate bonds had one of the worst starts of the year prior to the last 20 years. This was as a result of interest rates rising and increased investments into the stock markets. As less corporate bonds were issued, investors were expecting an increase in bond prices at the beginning of the year. However, this was not the case as companies with lower credit ratings replaced

technology companies on the market as “changes to US tax law allowed them to tap their offshore cash for activities they would previously fund with borrowing”.5

Highly rated US corporate bonds, borrowing at rates that are similar to the risk-free rate, have seen the most negative returns compared to other bonds, as many interest rate hikes have taken place recently. Moreover, as these bonds have the longest maturities, they are more sensitive to interest rate changes.

On a positive note, credit risk has decreased since the start of the year for investment grade bonds. However, “Investment-grade issuance has still been fairly aggressive, even though it’s down,” said Max Gokhman, head of asset allocation with Pacific Life Fund Advisors. “We’re definitely concerned about IG.”6

Our Bond Choices

Given your level of risk, we have specifically chosen bonds issued by highly reputable, majority “blue chip” companies. Almost all bonds in our portfolio are considered investment grade, with all but 2 exceptions, Netflix and Dell inc.- both of which shall be discussed.

Our fixed income portfolio comprises of 15 bonds from 5 different sectors: financial services, entertainment, mass merchants, energy and technology. These sectors were chosen given their lack of correlation to each other, mitigating risk and exposure to a single market. This acts as a hedge within the portfolio as any fluctuations in one

1 Lecture Notes 2 Schwab

3 CNBC

4 AAMLive

5 Financial Times 6 Financial Times

industry will not have the same effects on another industry, therefore it can offset the idiosyncratic risk to a particular firm/industry within this investment portfolio.

Investing in the Mass Merchants market (Amazon, Walmart, Target) can arguably be considered a defensive industry. This kind of industry is least affected by recessions and economic adversity, therefore during times of economic turmoil/uncertainty these companies will remain unaffected. This is because defensive industries make products which are necessity goods and mainly essentials.

Similarly, the Energy sector is also a defensive industry. For companies such as Exxon Mobil and Engie, who provide gas/oil, will less likely be affected as they are normal goods i.e. households use it for heating and gas. However, the inclusion of Tesla within this industry, deems a promising investment in the long term, where it is finding more sustainable methods of providing energy (Solar Panels) and producing electric vehicles which are environmentally friendly and cost effective in the long term.

Furthermore, the Financial Services sector is an interest sensitive industry- they are very sensitive to changes in interest rates. Given the current economic climate where interest rates are gradually rising in the US economy – ‘Short-term rates have slowly risen since then, by another 50 bps to 0.75% in late 2016, by an additional 75 bps to 1.50% in 2017, and by another 75 bps to 2.25% thus far in 2018.’ 7This could potentially lower bond prices as interest rates rise, however we decided to pick financial institutions who have performed well post financial crises. Furthermore, the financial institutions we have picked have ‘bonds which are rated from AAA down to BBB by credit ratings agencies such as Standard & Poor’s or Moody’s are classified as ‘investment grade’ and are deemed to be lower risk’. 8

The Technology sector includes the companies Apple, Microsoft Corporation and Dell. The technology sector is a great investment opportunity. It is the largest segment in the market and is associated with innovation and invention. Each sector in the economy requires and depends on technology to develop quickly and efficiently. On the equities side, technology prices fell. But the sector has performed relatively well in the fixed income market, which shows that investors are more worried about ‘the growth prospects of tech companies than their fundamental credit quality’9

The Entertainment sector is often considered as high risk, but along with high risk we have the possibility to make higher returns. However, we have chosen to invest in Walt Disney, Netflix, and 21st Century Fox as these companies are reputable ones with ratings ranging from B+ to A+. Moreover, there is a remarkable growth in the entertainment sector, as more and more people subscribe to streaming services such as Netflix. “Advances in mobile, video, and wireless technologies have ignited an explosion in the growth of streaming services. Nearly half of US households subscribed to one as of 2016, and 60 percent of US consumers (and 82 percent of millennials) stream TV shows at least monthly.”10

7 Forbes

8 Barclays – Smart Investor 9 WSJ

10 Deloitte

B- PortfolioOverview

Below we produced a table that consists of our 15 US corporate bonds, the bonds selected are all option free, US denominated bonds, thus par 100 = $1000. The table outlines the bond rating, coupon rate, maturity rate, accrued interest, modified duration, convexity, current yield and the yield to maturity. The market price and accrued interest given in the table are expressed in US $ value.

Bond Name

Apple Inc

AA+

878.55 3.45%

2/9/45 0.393% 127.94

AAA A+

B+ A BBB-

BBB AA+

All the bonds selected have a variety of maturity dates

have longer maturity whereas the lower rated bonds such as Netflix have shorter maturities. Of our 8 bonds that mature in 10+ years from our purchase, 6 of them are above A+. This allows for a lower default risk for longer term investments. The lowest grade bond according to the S&P rating in our portfolio is Netflix, rated B+. However, as per our fixed income portfolio strategy, this bond has the shortest maturity of 1 year from purchase (17/10/18)

Coupon Rate

In order to create a diverse portfolio where return is maximised but interest and reinvestment risk is minimised we chose 15 investment grade corporate bonds from 5 different sectors.

The bonds selected have different coupon rates with values ranging from 1.71%(Exxon) – 5.75%(Goldman Sachs). The coupon rate is the yield the bond paid on its issue date. 11 We chose a wide range of coupon rates because it creates a diversified portfolio. Low coupon rates are correlated with higher investment bond ratings thus safer investments where there is a low chance of bond default during a recession. On the other hand, a high coupon rate protects investors from interest risk and reinvestment risk, due to the coupons getting reinvested at the new forward rates, which may be higher than the existing rates. Thus protecting us from both aspects.

Microsoft Inc Dell Inc

Walt Disney The Company 21st Century Fox America

Netflix

Amazon.com Inc Target Corp

Walmart Inc Goldman Sachs

Group Inc JP Morgan Chase & Co Morgan Stanley

1063.18 4.50% 10/1/40 975.51 4.13% 6/1/44

987.7 5.88% 11/15/1 8

918.76 2.50% 4/15/26 1180.17 6.75% 10/1/37

948.41 3.95% 4/23/27 997.1 1.71% 3/1/19

0.423% 0.423%

0.595% 0.272% 0.572%

0.416% 0.171%

363.13 13.37 180.93 15.40

28.40 0.08

63.40 6.79 746.44 10.19

137.92 7.03 44.93 0.21

4.58% 4.14%

5.73% 2.50% 6.80%

4.00% 1.70%

264.98 337.12

74.55

57.23 176.68

64.97 0.49

17.25 3.50%

330.3

BB-

1010.37 4.63%

4/1/21 0.458% 349.32

2.05 4.84%

9.37

BBB+

1317.51 6.90%

8/15/39 0.524% 597.81

10.84 6.90%

210.9

AA-

979.71 1.90%

6/1/44 0.194% 8.44

18.12 1.91%

490.94

1291.3 6.50%

8/15/37 0.503% 725.83

10.65 6.51%

190.12

BBB+

984.28 3.88%

9/10/24 0.394% 159.74

5.28 3.97%

32.51

A-

977.92 2.88%

10/10/2 2

0.294% 173.70

3.73 3.20%

16.26

Engie Sa

Exxon Mobil Corporation Tesla Energy Operations

N/A

756.42 5.45%

1/14/31 0.720% 150.78

where the safer and higher rated bonds such as Apple Inc

8.73 5.45%

94.12

11 Investopedia

Rating (S&P)

Market Price

Coupon Rate

Maturity Date

Current yield

Accrued Interest

Modified Duration

YTM Convexity

Maturity

We chose bonds with a wide range of maturities therefore diversifying the portfolio.

As investors hold bonds for longer maturities, they expect to gain higher coupon rates. This is as they are more susceptible to default, thus require larger coupons rates to factor in default risk. Additionally, holding long term bonds also raises the concern for less liquidity, therefore higher coupon rates are also provided for long term bonds to account for liquidity premiums. Longer maturities are more likely to be affected by interest rate risks due to the greater chances of reinvestment fluctuations where they could lend at better rates if interest rates

rise. Additionally, the shorter maturity bonds correspond to increased liquidity and reduced default risk therefore they have lower coupon rates. Therefore, the pros and cons of both short term and long term maturities are offset.

Duration & Convexity

Duration is a measure of the sensitivity of the price of a bond to a change in interest rates. Duration takes into account the timing of the cash flows, giving more importance to cash flows in near rather than distant future. 12 Modified duration is just a simpler version to understand bond price volatility. ‘Investors with longer-duration loans—that is, holding longer-duration bonds—are more exposed to changes in interest rates than those with shorter-duration loans.’ 13Furthermore, convexity is a measure of the curvature in the relationship between bond prices and bond yields that demonstrates how the duration of a bond changes as the interest rate

changes. ‘Convexity is used as a risk-management tool, which helps measure and manage the amount of market risk to which a portfolio of bonds is exposed.’ 14 ‘The higher the convexity, the more dramatic the change in price given a move in interest rates’15

In our portfolio our modified duration values and convexity are diversified. Netflix has the lowest modified duration of 0.076, while Amazon has the highest one of 18.121, this is caused by a higher maturity date from Amazon and shorter maturity from Netflix. In addition, Exxon has the lowest convexity of 0.487, while Walt Disney has the highest value of 337.123. Through this diversification we can minimise the interest risk impact from future price changes thus allowing us to earn the required return with minimal risk.

Accrued Interest

Accrued Interest is the interest earned on a debt security which is yet to be collected. It is the interest that the seller will not receive from the issuer, as the issuer will send the next coupon payment to the buyer.16 The buyer then pays accrued interest to the seller calculated from the last coupon payment to settlement date. Therefore, the larger the semi-annual coupon rate (as there are semi-annual coupon periods), the larger the accrued interest required to the seller.

Current Yield & Yield to Maturity

Current Yield is the ratio of the coupon payment to the price of the bond. This represents the current yield return in this snapshot period. The current market price of a bond can be issued at discount, par or at a premium, therefore this can be a factor which alters if coupon rates are the same. However, the current yield only accounts for coupon income and no other source of income.

Therefore, the Yield-to-Maturity (YTM) is calculated. This is the interest rate that is earned if the bond is held to maturity given coupons payments are paid on time and reinvested at the same rates. This is a better measure of yield as it includes reinvestment income, however it is an approximation as future rates are unknown.

12 Lecture Notes 13 Vanguard

14 Investopedia 15 CFA Institute 16 Lecture Notes

C- Returnsanalysis

Yield Curve

To determine our yields to form an upward sloping curve we used Bloomberg to find the yield values from period 1 – period 53 (longest bond maturity) for each investment grading (e.g. yield average AAA rated bonds). From these values we were able to get an average value for each year and deduced an upward sloping yield curve with yield rates ranging from 3.3%-5.3%. The upward sloping yield curve begins to flatten after year 25 because the changes in the yields become smaller.

5.75 5.5 5.25 5 4.75 4.5 4.25 4 3.75 3.5 3.25 3

Years to Maturity

Using our predicted yield rates, we were able to deduce our reinvestment income, total income, price appreciation and depreciation and holding price return as shown in the table below.

Income & Return

Company Name

Coupon Income

Apple Inc

Reinvestment Total Income Income

Selling Purchase Price Price

Holding Period Price Return Change

345.00

82.85

427.85

802.32

878.55

1.70%

-8.68%

Microsoft Inc

450.00

108.06

558.06

926.01

1063.18

1.68%

-12.90%

Dell Inc

138.75

417.57

99.06

556.32

1000.00

1010.37

2.18%

1.79%

-1.03%

Walt Disney The

Company

412.50

511.56

878.58

975.51

-9.94%

21st Century Fox America

690.00

165.70

855.70

1131.41

1317.51

2.08%

-14.12%

Netflix

588.00

141.20

729.20

1005.13

987.7

2.85%

1.76%

Amazon.com Inc

190.00

45.63

235.63

639.73

979.71

-0.56%

-34.70%

Target Corp

200.00

193.36

393.36

1000.00

918.76

2.10%

8.84%

Walmart Inc

650.00

156.09

806.09

1089.98

1291.3

1.94%

-15.59%

Goldman Sachs Group Inc

675.00

162.10

837.10

1107.82

1180.17

2.53%

-6.13%

JP Morgan Chase & Co

232.50

280.12

512.62

1000.00

984.28

2.17%

1.60%

Yield %

Morgan Stanley

355.50

142.76

498.26

1000.00

948.41

2.31%

5.44%

Engie Sa

115.00

351.57

466.57

1000.00

977.92

2.05%

2.26%

Exxon Mobil Corporation

8.45

459.42

467.87

1000.00

997.1

1.95%

0.29%

Tesla Energy Operations

547.00

130.88

677.88

1013.37

756.42

4.11%

33.97%

We decided to choose a 10-year investment horizon, therefore 6 of our 15 bonds were sold at par ($1000) because they expired before our investment horizon.

Coupon income is calculated as the actual coupon cash flow multiplied by the number of periods in which they will be received.

The reinvestment income is also known as ‘interest on interest.’ Calculations for reinvestment income differ for short term (less than the investment horizon) and long term maturity bonds. For bonds that expire before our investment horizon, we have assumed that we will re-invest the coupons and par value at our deduced (upward sloping) yields until the end of our investment horizon. For bonds that have a longer maturity than our investment horizon, we have assumed that we will reinvest the coupons until the end of our investment horizon and then sell these bonds. Therefore, for shorter term bonds the reinvestment income is higher as we also add in the reinvestment income received from the par value received upon expiry.

The selling price is computed as the sum of the present values of the future coupons. We sum the coupon income and reinvestment income to find total income from our bonds.

Our annualized holding period return is calculated as follows:

[𝑇𝑜𝑡𝑎𝑙 𝐼𝑛𝑐𝑜𝑚𝑒 + 𝑆𝑒𝑙𝑙𝑖𝑛𝑔 𝑃𝑟𝑖𝑐𝑒]1/20 − 1 𝑃𝑢𝑟𝑐h𝑎𝑠𝑒 𝑃𝑟𝑖𝑐𝑒

Tesla has the highest holding period of 4.11% while Amazon has the lowest holding period of -0.56%. The negative holding period return for Amazon is due to the large decrease in price of 34.7%.

D- Interest Rate & Reinvestment Risk Immunisation

Long Portfolio with 4% Yield

Bond prices and interest rates have an inverse relationship: if interest rates go up, bond prices decrease and vice versa. Interest rate changes also affect the reinvestment of our coupons, but it is a positive relationship, as interest rates increase, the return on our invested coupons will also increase. These opposing relationships create a risk for our portfolio.

Immunisation is an investment strategy that locks in a fixed rate of return over our investment horizon. When the portfolio duration and investment horizon are equal, price volatility and reinvestment risk are exactly offset: interest rate fluctuations will affect the bonds’ prices and the reinvestment of their coupons at the same rate, locking in the portfolio’s rate of the return at a fixed rate.

A key assumption in the immunisation of this portfolio is that our investment horizon does not change. We have constructed our portfolio based on an investment horizon of 10 years, if this is changed, the portfolio will no longer become valid for immunisation and would have to be recalculated.

To immunise our bond portfolio from interest rate and reinvestment risk, while maintaining our desired 4% yield we carried out the following process;

1. We have designed this portfolio that equalises our weighted portfolio duration (using our previously calculated durations assuming a flat yield curve) with our investment horizon of 10 years.

2. The sum of our weighted portfolio yields use our 4% desired yield.

3. Our bond weights do not exceed 25% in any single bond, maintaining its diversity to reduce the portfolio

risks.

4. The sum of our weighted portfolio was equal to 1.

Apple Inc Microsoft Inc Dell Inc Walt Disney The Company 21st Century Fox America Netflix Amazon.com Inc Target Corp Walmart Inc Goldman Sachs Group Inc

E- PortfolioYieldMaximisation

Name Weights YTM

25.00%

4.22%

5.63%

6.22% 11.24% 2.09% 4.28% 2.20% 11.14%

4.06% 0.23% 4.28% 0.26% 6.04% 0.68% 3.75% 0.08% 5.24% 0.22% 4.69% 0.10% 2.49% 0.28%

1.06%

9.81%

4.18%

0.41%

4.71%

4.53%

0.21%

8.46%

2.00%

0.17%

4.49%

4.24%

0.19%

1.36%

4.18%

0.06%

JP Morgan Chase & Co Morgan Stanley Engie Sa Exxon Mobil Corporation Tesla Energy Operations

0.65%

3.47%

0.02%

To allow our client to maximise yield while being immune to interest and reinvestment risk we used the immunisation strategy. For this strategy we constructed two portfolios one with short selling bonds and one without short selling bonds.

Long Portfolio with Maximum Yield

2.71%

8.73%

0.24%

Portfolio 1 4.21%

4.21%

Name

Weights Weighted Convexity Weighted YTM

Weighted Modified Duration

Apple Inc

6.27%

20.704

0.26%

1.026

Microsoft Inc

5.04%

13.356

0.20%

0.711

Dell Inc

0.00%

0.000

0.00%

0.000

Walt Disney The Company

7.72%

26.010

0.33%

1.184

21st Century Fox America

5.91%

12.467

0.27%

0.721

Netflix

1.00%

0.745

0.06%

0.001

Amazon.com Inc

0.00%

0.000

0.00%

0.000

Target Corp

0.00%

0.000

0.00%

0.000

Walmart Inc

3.95%

7.518

0.17%

0.464

Goldman Sachs Group Inc

8.79%

15.534

0.46%

0.993

JP Morgan Chase & Co

0.00%

0.000

0.00%

0.000

Morgan Stanley

2.63%

1.711

0.12%

0.184

Engie Sa

0.00%

0.000

0.00%

0.000

Exxon Mobil Corporation

0.00%

0.000

0.00%

0.000

Tesla Energy Operations

58.69%

55.234

5.12%

4.716

Portfolio

1 153.278 7%

The above portfolio provides us with a 7%, 3% higher than required. Whilst the highest return could be around 8.7% from Tesla alone, this does not immunise against interest rate risks. Thus, we based this portfolio around ensuring all sectors are incorporated, providing diversification in various markets. However, in order to increase our yield to 7%, a greater weight has been given to Tesla. Our original long only portfolio had given Tesla a weight of 2.7%. In order to maximise yield return, this had to be increased to 58.7%. We understand that it is not realistic to invest such a

Weighted YTM

large proportion in one bond, however, this combination provides the highest return whilst including bonds from each sector. This portfolio is constructed using fewer securities. Due to their lower yields, Dell Inc, Amazon, Target, JP Morgan, Engie and Exxon Mobil are not included within this maximum yield portfolio.

Effect of a 1% increase in interest rates

This portfolio’s riskiness can be calculated as the sum of the predicted price change by duration and by convexity. Predicted price change by duration: (−𝑀𝑜𝑑𝑖𝑓𝑖𝑒𝑑 𝐷𝑢𝑟𝑎𝑡𝑖𝑜𝑛) × ∆𝐼𝑛𝑡𝑒𝑟𝑒𝑠𝑡 𝑅𝑎𝑡𝑒 × 100

= −10 × 0.01 × 100 = −10% change in the portfolio price.

The price change predicted by Convexity:𝐶𝑜𝑛𝑣𝑒𝑥𝑖𝑡𝑦⁄2 × 𝑑𝑦2 × 100 = (153.28⁄2) × 0.012 × 100 = 0.7664%

change in the portfolio price.

Therefore, the price change predicted by duration and convexity is:

−10 + 0.7664 = −9.23%

For this portfolio, a 1% increase in interest rates suggests a 9.23% decrease in our portfolio price.

Given we have immunised this portfolio by matching the portfolio’s modified duration to our investment horizon, this fall in price will be offset by the increased reinvestment income from future coupon payments.

Short Portfolio with Maximum Yield

Name

Weights Weighted Convexity Weighted YTM

Weighted Modified Duration

Apple Inc

23%

75.93

0.97%

3.76

Microsoft Inc

-30%

-79.49

-1.22%

-4.23

Dell Inc

30%

2.81

1.25%

0.69

Walt Disney The Company

30%

101.14

1.28%

4.60

21st Century Fox America

30%

63.27

1.36%

3.66

Netflix

30%

22.37

1.81%

0.02

Amazon.com Inc

-30%

-147.28

-0.60%

-6.00

Target Corp

-30%

-17.17

-1.13%

-2.02

Walmart Inc

30%

57.04

1.27%

3.52

Goldman Sachs Group Inc

30%

53.00

1.57%

3.39

JP Morgan Chase & Co

-13%

-4.22

-0.54%

-0.67

Morgan Stanley

30%

19.49

1.41%

2.09

Engie Sa

-30%

-4.88

-1.04%

-1.12

Exxon Mobil Corporation

-30%

-0.15

-0.75%

-0.11

Tesla Energy Operations

30%

28.24

2.62%

2.41

Portfolio

1 170.09 8.27%

Without constraining the weights, we could have achieved a return of 11%, however this portfolio structure would not have been realistic as it involved shorting up to 67% of our funds in one bond and investing 76% in another. Therefore, we have set a shorting limit of 30% of our funds in any single bond in order to protect ourselves from making large losses as our liabilities would not exceed our assets. We have also set a limit of 30% to be invested in any single bond to maintain a diversified portfolio and reduce any company specific risks. In fact, by putting a 30% constraint on our weights, all of our bonds participate in our portfolio, in which we shorted 6 bonds and took a long position in the remaining 9 bonds.

This portfolio allows short-selling and therefore provides us a higher return of 8.27%. This portfolio is immune to reinvestment and interest rate risk, as well as specific risk as it is composed of bonds from every sector. However, it is subject to other risks related to short-selling.

Risks & Drawbacks of Short-Selling

As an individual investor you may not be able to short sell a bond. ‘To do so would require locating an existing holder of that bond and then borrowing it from them in order to sell it in the market.’17 However, while short selling of a bond can provide higher returns, it presents many risk and drawbacks.

Like many other securities, bonds experience price fluctuations in relation to the market. In order to short a bond, we must agree to sell the bond at the current market price and repurchase it either at an unknown or given time in the future. The goal is to repurchase the bond at a lower price. We short bonds in hopes that future interest rates will rise thus lowering the bond price.18 However, in an event where interest rates may fall, we will be obliged to purchase the bond at a greater price, leading to a capital loss.

In extreme cases this is called a “short squeeze”, whereby the sudden increase in the security price (which we are short) causes panic and uncertainty due to the repurchase agreement. This strategy of short selling a bond leaves our portfolio exposed to interest rate risk, hence we have also created a maximum yield long only portfolio, where immunisation allows us to benefit from potential increases in interest rates via increased cash flow from reinvestments of coupons.

Another drawback of short selling a bond is that the investor should have a margin account- this means investors must set aside capital as collateral in the case of rising bond prices. ‘The Federal Reserve Board’s Regulation T requires short sellers to deposit collateral, called margin, with the broker in the amount of 150 percent of the initial value of the shorted securities.’ In an event where bond prices increase, you will ‘receive a margin call from your broker to put up extra margin.’19 If additional margin is not added, your bond position is liquidated leading to a capital loss. Margin accounts also expose investors to leverage, which if not adequately managed and hedged, can increase our risk exposure.

Effect of a 1% increase in interest rates

The riskiness of a portfolio can be shown by the change in price predicted by duration and convexity following a 1% change in interest rates which is calculated as the sum of the price change predicted by duration

(−𝑀𝑜𝑑𝑖𝑓𝑖𝑒𝑑 𝐷𝑢𝑟𝑎𝑡𝑖𝑜𝑛) × ∆𝐼𝑛𝑡𝑒𝑟𝑒𝑠𝑡 𝑅𝑎𝑡𝑒 × 100 = −10 × 0.01 × 100 = −10% and the price change predicted

by convexity 𝐶𝑜𝑛𝑣𝑒𝑥𝑖𝑡𝑦⁄2 × 𝑑𝑦2 × 100 = (170.09⁄2) × 0.012 × 100 = 0.85%. Therefore, the price change predicted by Duration and Convexity is

−10 + 0.85 = −9.15%

For this portfolio, a 1% increase in interest rates suggests a 9.15% decrease in our portfolio price.

F- Conclusion&Recommendations

With the 10-year investment horizon, 4% required yield and a risk neutral approach, this fund management team would recommend taking a long only position to maximise yield. Whilst the short-selling inclusive portfolio raises a higher yield, there are many uncertainties with this investment strategy such as short squeezes. Additionally, to limit these short selling exposures- constraints were introduced. However, there remains a short exposure of -163%, which increases the risk exposure of the portfolio. Therefore, we would recommend holding a long only portfolio which provides a 7% YTM (3% above required yield), with a diversified portfolio holding at least one bond from each industry with more realistic weights and removing exposures of short-selling whilst remaining immunised.

17 Investopedia 18 Investopedia 19 Zacks

References

Anon, (2018). [online] Available at: https://www.aamlive.com/blog/201802/corporate-bonds-a-review-of-2017-and- a-look-forward-into-2018 [Accessed 14 Nov. 2018].

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