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Instructions:
Financial Risk Management is an essential aspect of any financial institution. It involves identifying, measuring, and mitigating risks that may arise in financial markets. Internal aspects of financial institutions include identifying risks in credit and operational risk, as well as managing liquidity, market, and interest rate risk.
External factors that affect the investment arena and modern financial markets include macroeconomic events such as changes in interest rates, inflation rates, and political instability. Financial risk management involves understanding how these factors impact investments and developing strategies to manage these risks.
Theoretical foundations that underpin modern investment and risk management techniques include portfolio theory, option pricing theory, and capital asset pricing models. Understanding these theories can help in developing investment strategies and managing risks.
The practical dimension of financial risk management involves applying theoretical knowledge to real-world scenarios. This includes developing investment strategies that incorporate risk management techniques, analyzing financial data, and using financial models to make informed decisions.
Overall, a degree in Financial Risk Management can provide you with a solid understanding of the theoretical foundations of modern investment and risk management techniques, as well as practical skills that can be applied to equity and credit markets. This can help in developing effective investment strategies and managing risks in financial markets.
Your friend is celebrating her 35 th birthday today and wants to start saving for her anticipated retirement at age 65 (she will retire on her 65 th birthday). She would like to be able to withdraw $\$ 80,000$ from her savings account on each birthday for at least 20 years following her retirement (the first withdrawal will be on her 66th birthday). Your friend intends to invest her money in the local savings bank which offers 4 percent per year. She wants to make equal annual deposits on each birthday in a new savings account she will establish for her retirement fund.
If she starts making these deposits on her 36 th birthday and continues to make deposits until she is 65 (the last deposit will be on her 65 th birthday), what amount must she deposit annually to be able to make the desired withdrawals upon retirement?
To determine the amount your friend must deposit annually, we can use the concept of present value, which is the current value of a future sum of money after accounting for the time value of money.
We know that your friend wants to withdraw $80,000 per year for at least 20 years after her retirement, and the first withdrawal will be on her 66th birthday. Assuming that she lives for 20 years after the first withdrawal, the total number of withdrawals she will make is:
20years+1=21withdrawals
We can use the formula for present value of an annuity to determine how much she needs to deposit each year to be able to make these withdrawals. The formula is:
$P V=\frac{P M T}{r}\left[1-\frac{1}{(1+r)^n}\right]$
where PV is the present value of the annuity, PMT is the annual payment, r is the interest rate, and n is the number of periods.
In this case, we want to find the PMT, which represents the annual deposit your friend must make. We know that:
- The interest rate is 4% per year
- The number of periods is 21 (from her 45th birthday to her 65th birthday)
- The future value of the annuity is the total amount she will withdraw over 20 years, which is:$F V=20 \times \$ 80,000=\$ 1,600,000$
Substituting these values into the formula, we get:
$P V=\frac{\mathrm{PMT}}{0.04}\left[1-\frac{1}{(1+0.04)^{21}}\right]=\$ 1,600,000$
Solving for PMT, we get:
$\mathrm{PMT}=\frac{\$ 1,600,000 \times 0.04}{1-\frac{1}{(1+0.04)^{21}}} \approx \$ 36,044.68$
Therefore, your friend must deposit approximately $$36,044.68$ each year from her 36th birthday to her 65th birthday to be able to withdraw $$80,000$ per year for at least 20 years after her retirement.
The current level of the S\&P 500 is 1040 . The risk-free interest rate per year is $2 \%$. Assume negligible dividends. The 6 month futures contract is trading at 1060 . (a)Is there an arbitrage opportunity? Briefly explain.
(a) To determine if there is an arbitrage opportunity, we can calculate the theoretical futures price using the cost-of-carry model:
$\mathrm{F}=\mathrm{S}^* \mathrm{e}^{\wedge}\left(r^{\star} \mathrm{t}\right)$
where F is the theoretical futures price, S is the current spot price, r is the risk-free interest rate, and t is the time to expiration in years.
In this case, the time to expiration is 0.5 years, and the risk-free interest rate is 2%. Plugging in the values, we get:
$F=1040 * e^{\wedge}(0.02 * 0.5)=1051.2$
Since the current futures price is 1060, there is an arbitrage opportunity. The theoretical futures price is lower than the current futures price, which means we can make a riskless profit by using the cost-of-carry model.
(b)If there is an arbitrage opportunity, what strategy would you use to exploit it without using any funds of your own?
(b) To exploit the arbitrage opportunity without using any funds of our own, we can use a cash-and-carry arbitrage strategy. The steps involved are:
- Borrow money to buy the underlying asset (in this case, the S&P 500 index) at the spot price.
- Sell a futures contract for the same asset, and receive the current futures price.
- Invest the proceeds from the futures sale at the risk-free rate.
- When the futures contract expires, take delivery of the underlying asset and use it to repay the loan.
Since the theoretical futures price is lower than the current futures price, we can use the cash-and-carry arbitrage strategy to lock in a profit. Here’s how it works:
- Borrow $1040 to buy the S&P 500 index at the current spot price.
- Sell a futures contract for the S&P 500 index at the current futures price of $1060.
- Invest the $1060 at the risk-free rate of 2% for 6 months, which gives us:
- $ 1060 * \mathrm{e}^{\wedge}(0.02 * 0.5)=\$ 1071.21$
- When the futures contract expires in 6 months, take delivery of the S&P 500 index and use it to repay the loan of $1040.The profit from this strategy is:
- Profit $=\$ 1071.21-\$ 1040=\$ 31.21$
- Since we didn’t use any of our own funds to execute this strategy, the profit is risk-free.
